158edo

158edo is the equal division of the octave into 158 parts of 7.594937 cents each. It is inconsistent to the 5-limit and higher limit, with five mappings possible for the 13-limit: <158 250 367 444 547 585| (patent val), <158 251 367 444 547 585| (158b), <158 250 366 443 546 584| (158cdef), <158 250 367 443 546 585| (158de), and <158 250 367 443 546 584| (158def). Using the patent val, it tempers out the Würschmidt comma, 393216/390625 and 3486784401/3355443200 in the 5-limit; 225/224, 8748/8575, and 40960000/40353607 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 19683/19208 in the 11-limit, providing the optimal patent val for the 11-limit marvolo temperament; 144/143, 640/637, 2025/2002, 2200/2197 and 3159/3125 in the 13-limit. Using the 158b val, it tempers out the diaschisma, 2048/2025 and |-1 -33 23> in the 5-limit; 245/243, 6144/6125 and 2500000/2470629 in the 7-limit; 1331/1323, 1375/1372, 2560/2541, and 4375/4356 in the 11-limit; 364/363, 572/567, 625/624, 640/637, and 1625/1617 in the 13-limit. Using the 158cdef val, it tempers out the small diesis, 3125/3072 and the lalagu comma, 43046721/41943040 in the 5-limit; 2401/2400, 19683/19600, and 78125/76832 in the 7-limit; 243/242, 441/440, 4000/3993, and 33275/32768 in the 11-limit; 325/324, 975/968, 1287/1280, 1573/1568, and 1875/1859 in the 13-limit, supporting the 13-limit harry temperament. Using the 158de val, it tempers out 126/125, 33075/32768, and 118098/117649 in the 7-limit; 243/242, 385/384, 1617/1600, and 117649/117128 in the 11-limit; 196/195, 351/350, 1287/1280, 1575/1573, and 4455/4394 in the 13-limit. Using the 158def val, it tempers out 676/675, 847/845, 1573/1568, 1701/1690, and 3159/3136 in the 13-limit.

158edo can be treated as the 2.9/5.11/7.13/7 subgroup temperament with patent 9, which tempers out 9801/9800, 35750/35721, and |-1 0 0 4 -19 15>.